A new simple dynamo model for stellar activity cycle

Nobumitsu Yokoi, Dieter Schmitt, Valery Pipin, Fujihiro Hamba

Published 2016-01-24Version 1

A new simple dynamo model for stellar activity cycle is proposed. By considering an inhomogeneous mean flow effect on turbulence, it is shown that turbulent cross helicity (velocity--magnetic-field correlation) should enter the expression of turbulent electromotive force as the coupling coefficient for the mean absolute vorticity. The inclusion of the cross-helicity effect makes the present model different from the current $\alpha$--$\Omega$-type models mainly in two points. First, in addition to the usual $\alpha$ (helicity effect) and $\beta$ (turbulent magnetic diffusivity), we consider the $\gamma$ coefficient (cross-helicity effect). Second, unlike the $\alpha$ and $\beta$ coefficients, which are often treated as an adjustable parameter in the current studies, the spatiotemporal evolution of $\gamma$ coefficient should be solved simultaneously with the mean magnetic-field equations. The basic scenario for the stellar activity cycle in the present model is as follows: In the presence of turbulent cross helicity, the toroidal field is induced by the toroidal rotation in mediation by the turbulent cross helicity. Then, as usual models, the $\alpha$ or helicity effect generates the poloidal field from the toroidal one. This poloidal field, induced by the $\alpha$ effect, produces a turbulent cross helicity whose sign is opposite to the original one (negative production of cross helicity). The cross helicity with the opposite sign starts producing a reversed toroidal field. Eigenvalue analyses of the simplest possible present model give a butterfly diagram, which confirms the above scenario as well as the equator-ward migrations, the phase relationship between the cross helicity and magnetic fields, etc.